Unirationality of the Hurwitz space $$\varvec{\mathcal {H}_{9,8}}$$ H 9 , 8

2017 ◽  
Vol 109 (6) ◽  
pp. 511-519
Author(s):  
Hamid Damadi ◽  
Frank-Olaf Schreyer
Keyword(s):  
Hurwitz Space

scholarly journals The uniformization of the moduli space of principally polarized abelian 6-folds

2020 ◽  
Vol 2020 (761) ◽  
pp. 163-217
Author(s):  
Valery Alexeev ◽  
Ron Donagi ◽  
Gavril Farkas ◽  
Elham Izadi ◽  
Angela Ortega
Keyword(s):  
Weyl Group ◽  
Abelian Variety ◽  
Moduli Space ◽  
Projective Line ◽  
Geometric Description ◽  
Canonical Class ◽  
Hurwitz Space ◽  
The Way

AbstractStarting from a beautiful idea of Kanev, we construct a uniformization of the moduli space \mathcal{A}_{6} of principally polarized abelian 6-folds in terms of curves and monodromy data. We show that the general principally polarized abelian variety of dimension 6 is a Prym–Tyurin variety corresponding to a degree 27 cover of the projective line having monodromy the Weyl group of the E_{6} lattice. Along the way, we establish numerous facts concerning the geometry of the Hurwitz space of such E_{6}-covers, including: (1) a proof that the canonical class of the Hurwitz space is big, (2) a concrete geometric description of the Hodge–Hurwitz eigenbundles with respect to the Kanev correspondence and (3) a description of the ramification divisor of the Prym–Tyurin map from the Hurwitz space to \mathcal{A}_{6} in the terms of syzygies of the Abel–Prym–Tyurin curve.

scholarly journals Connected Components of H_(r,g)^A (G)

2018 ◽  
Vol 22 (2) ◽  
pp. 106
Author(s):  
Haval M. Mohammed Salih
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Monodromy Group ◽  
Riemann Sphere ◽  
Primitive Group ◽  
Connected Components ◽  
Branch Points ◽  
Genus Zero ◽  
Hurwitz Spaces ◽  
Hurwitz Space

The Hurwitz space   is the space of genus g covers of the Riemann sphere  with  branch points and the monodromy group . In this paper, we enumerate the connected components of the Hurwitz spaces  for a finite primitive group of degree 7 and genus zero except . We achieve this with the aid of the computer algebra system GAP and the MAPCLASS package.

scholarly journals Reduction of the Hurwitz space of metacyclic covers

2004 ◽  
Vol 121 (1) ◽  
pp. 75-111 ◽  
Author(s):  
Irene I. Bouw
Keyword(s):  
Hurwitz Space

Every curve is a Hurwitz space

1989 ◽  
Vol 59 (3) ◽  
pp. 737-746 ◽  
Author(s):  
Steven Diaz ◽  
Ron Donagi ◽  
David Harbater
Keyword(s):  
Hurwitz Space

scholarly journals Connected Components of the Hurwitz Space for the Symmetric Group of Degree 7

2020 ◽  
Vol 24 (2) ◽  
pp. 129
Author(s):  
Haval M. Mohammed Salih
Keyword(s):  
Symmetric Group ◽  
Monodromy Group ◽  
Riemann Sphere ◽  
Complete Classification ◽  
Connected Components ◽  
Branch Points ◽  
Genus Zero ◽  
Computational Tools ◽  
Hurwitz Space

The Hurwitz space  is the space of genus  covers of the Riemann sphere  with branch points and the monodromy group . Let be the symmetric group . In this paper, we enumerate the connected components of . Our approach uses computational tools, relying on the computer algebra system GAP and the MAPCLASS package, to find the connected components of . This work gives us the complete classification of  primitive genus zero symmetric group of degree seven. 

scholarly journals A COMPACTIFICATION OF THE HURWITZ SPACE

Topology ◽  
1999 ◽  
Vol 38 (4) ◽  
pp. 889-914 ◽  
Author(s):  
Sergei Natanzon ◽  
Vladimir Turaev
Keyword(s):  
Hurwitz Space
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